Finite Group Databasebeta

← #11660225

Subgroups — #11660225

Order 768.

1658 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#235C211yesmaximal, characteristic
2C3×Q8×M16C211yesmaximal, characteristic, complemented
3C2×#5024C211yesmaximal, characteristic, complemented
4#79968C214yesmaximal, complemented
5#79966C214yesmaximal, complemented
6#79964C212yesmaximal, complemented
7#79963C212yesmaximal, complemented
8#79923C212yesmaximal, complemented
9#79922C212yesmaximal, complemented
10#79045C212yesmaximal, complemented
11#79044C211yesmaximal, characteristic, complemented
12#79040C212yesmaximal
13#79040C211yesmaximal, characteristic
14#78520C212yesmaximal
15#78519C211yesmaximal, characteristic
16#78508C212yesmaximal, complemented
17#78508C211yesmaximal, characteristic, complemented
18#60254—31nomaximal, Sylow
19C2×C3×C4×Q8C2211yescharacteristic
20Q8×#67C412yes—
21#5579C411yescharacteristic
22#5579C412yes—
23#5578C2212yes—
24#5578C2214yes—
25Q8×D12C411yescharacteristic
26C4×D3×Q8C2212yes—
27#5567C411yescharacteristic
28#5567C412yes—
29Q8×Dic6C411yescharacteristic
30#5511C412yes—
31#5511C414yes—
32C4×#235C2211yescharacteristic
33C4×#235C2212yes—
34#5470C2211yescharacteristic
35#5470C2212yes—
36C3×#446C2212yes—
37C3×#446C2214yes—
38C3×C8×Q8C2212yes—
39C3×#423C2211yescharacteristic
40C3×#423C2212yes—
41C3×C4×M16C2211yescharacteristic
42C3×C4×M16C2212yes—
43#5129C2211yescharacteristic
44#5129C2211yescharacteristic
45#5129C2212yes—
46#5122C2212yes—
47#5122C2212yes—
48#5122C2212yes—
49#5119C2211yescharacteristic
50#5119C2212yes—
51#5119C2211yescharacteristic
52#5119C2212yes—
53#5024C2211yescharacteristic
54#5024C2211yescharacteristic
55#5024C2211yescharacteristic
56#5024C2211yescharacteristic
57#5024C2212yes—
58#5024C2212yes—
59C2×C4⋊(C3⋊C8)C2211yescharacteristic
60C2×C4⋊(C3⋊C8)C2212yes—
61C2×#803C2212yes—
62C2×C4×C3⋊C8C2211yescharacteristic
63#4840C2214yes—
64#4840C2214yes—
65#4840C2214yes—
66#4835C2212yes—
67#4835C2214yes—
68#4833C2212yes—
69#4833C2214yes—
70#4831C2212yes—
71#4831C2212yes—
72#4830C2212yes—
73#4830C2212yes—
74#4828C2214yes—
75#4828C2214yes—
76#4828C2214yes—
77#4828C2214yes—
78#4709C2212yes—
79#4709C2212yes—
80#4705C2214yes—
81#4705C2214yes—
82#4701C2214yes—
83#4701C2214yes—
84#4701C2214yes—
85#4690C2214yes—
86#4690C2214yes—
87#4685C2212yes—
88#4685C2212yes—
89#4679C2214yes—
90#4679C2212yes—
91C8×Dic6C2212yes—
92C8×Dic6C2214yes—
93Q8×#41—31no—
94#2987—34no—
95#2986—32no—
96#2985—34no—
97#2985—32no—
98#2984—32no—
99#2983—32no—
100Q8×M16D311yescharacteristic, complemented
101#2962—31no—
102#2962—32no—
103#2961—32no—
104#2960—31no—
105C2×#446—31no—
106#2925—31no—
107#2925—32no—
108#2923—32no—
109#2922—31no—
110C22×C3×Q8C2×C411yescharacteristic
111C2×D3×Q8C2×C412yes—
112C2×#235C2311yescharacteristic
113C2×C3×M16C2312yes—
114C2×C3×M16C2311yescharacteristic
115C2×C3×M16C2311yescharacteristic
116C3×C4×Q8C2×C411yescharacteristic
117C3×C4×Q8C2×C411yescharacteristic
118C3×C4×Q8C2×C412yes—
119C3×C4×Q8C2311yescharacteristic
120C3×C4×Q8C2311yescharacteristic
121C3×C4×Q8C2312yes—
122C2×C3×C4⋊C4C2×C411yescharacteristic
123C2×C3×C4⋊C4C2×C412yes—
124C2×C3×C42C2311yescharacteristic
125C2×C3×C42C2312yes—
126#946C2×C412yes—
127#946C2×C414yes—
128Q8×Dic3C2×C412yes—
129#944C2×C412yes—
130#944C2×C414yes—
131C4×#67C2×C412yes—
132C4×#67C2×C414yes—
133C4×#67C2×C412yes—
134C4×#67C2×C414yes—
135#926C2312yes—
136#926C2311yescharacteristic
137#924C2×C412yes—
138#924C2×C414yes—
139#924C2×C412yes—
140#924C2×C414yes—
141C22×C3⋊C8C2311yescharacteristic
142C22×C3⋊C8C2312yes—
143C22×C3⋊C8C2311yescharacteristic
144#897C2×C412yes—
145#897C2×C414yes—
146#896C2×C414yes—
147#896C2×C414yes—
148#896C2×C414yes—
149D3×C4⋊C4C2×C412yes—
150D3×C4⋊C4C2×C414yes—
151#889C2×C414yes—
152#889C2×C414yes—
153#889C2×C414yes—
154#888C2×C412yes—
155#888C2×C414yes—
156#887C2×C412yes—
157#887C2×C414yes—
158C4×D12C2×C411yescharacteristic
159C4×D12C2×C412yes—
160C4×D12C2×C411yescharacteristic
161C4×D12C2×C412yes—
162#872C2314yes—
163#872C2312yes—
164C42×D3C2312yes—
165C42×D3C2314yes—
166#870C2×C412yes—
167#870C2×C412yes—
168#870C2×C412yes—
169#869C2×C411yescharacteristic
170#869C2×C412yes—
171#869C2×C411yescharacteristic
172#869C2×C412yes—
173C4×Dic6C2×C411yescharacteristic
174C4×Dic6C2×C412yes—
175C4×Dic6C2×C411yescharacteristic
176C4×Dic6C2×C412yes—
177C4×Dic6C2312yes—
178C4×Dic6C2314yes—
179C4×Dic6C2314yes—
180C4×Dic6C2312yes—
181C3×C4⋊C8C2314yes—
182C3×C4⋊C8C2312yes—
183C3×C4⋊C8C2314yes—
184C3×C4⋊C8C2312yes—
185C3×#97C2314yes—
186C3×#97C2312yes—
187C3×C4×C8C2312yes—
188C3×C4×C8C2314yes—
189(C2×D3)⋊C8C2312yes—
190(C2×D3)⋊C8C2312yes—
191(C2×D3)⋊C8C2312yes—
192(C2×D3)⋊C8C2312yes—
193(C2×D3)⋊C8C2314yes—
194(C2×D3)⋊C8C2314yes—
195#815C2314yes—
196#815C2314yes—
197#815C2314yes—
198Dic3⋊C8C2312yes—
199Dic3⋊C8C2314yes—
200Dic3⋊C8C2314yes—
201Dic3⋊C8C2312yes—
202Dic3⋊C8C2312yes—
203Dic3⋊C8C2312yes—
204Dic3⋊C8C2314yes—
205Dic3⋊C8C2314yes—
206C8×Dic3C2314yes—
207C8×Dic3C2314yes—
208C8×Dic3C2314yes—
209C4⋊(C3⋊C8)C2311yescharacteristic
210C4⋊(C3⋊C8)C2312yes—
211C4⋊(C3⋊C8)C2311yescharacteristic
212C4⋊(C3⋊C8)C2312yes—
213C4⋊(C3⋊C8)C2312yes—
214C4⋊(C3⋊C8)C2312yes—
215C4⋊(C3⋊C8)C2312yes—
216#803C2312yes—
217#803C2312yes—
218#803C2312yes—
219#803C2312yes—
220C4×C3⋊C8C2311yescharacteristic
221C4×C3⋊C8C2311yescharacteristic
222C4×C3⋊C8C2311yescharacteristic
223C4×C3⋊C8C2311yescharacteristic
224Q82—31no—
225#557—31no—
226#557—32no—
227#554—31no—
228#554—32no—
229#554—32no—
230#554—34no—
231D4×Q8—32no—
232D4×Q8—31no—
233#533—32no—
234#533—34no—
235#533—31no—
236#533—32no—
237C4×#41—31no—
238C4×#41—32no—
239C2×C4×Q8—32no—
240C2×C4×Q8C2×D311yescharacteristic
241#446—31no—
242#446—31no—
243#446—31no—
244#446—32no—
245#446—31no—
246#446—32no—
247#446—32no—
248#446—32no—
249#446—34no—
250#446—34no—
251#446—34no—
252#446—34no—
253#446—34no—
254#446—34no—
255#446—34no—
256#446—32no—
257#446—34no—
258#446C2×D312yes—
259#446C2×D314yes—
260C8×Q8—32no—
261C8×Q8—32no—
262C8×Q8—32no—
263C8×Q8—34no—
264C8×Q8C2×D312yes—
265#433—34no—
266#433—34no—
267#433—34no—
268#433—32no—
269#433—32no—
270#433—34no—
271#433—34no—
272#432—34no—
273#432—32no—
274#432—34no—
275#432—34no—
276#431—32no—
277#431—34no—
278#431—32no—
279#431—32no—
280#424—31no—
281#424—31no—
282#424—32no—
283#424—32no—
284#423C2×D311yescharacteristic
285#423C2×D312yes—
286C2×C4⋊C8—31no—
287C2×C4⋊C8—32no—
288#408—31no—
289#408—31no—
290#408—32no—
291#405—32no—
292#405—32no—
293#405—32no—
294C4×M16C2×D311yescharacteristic
295C4×M16C2×D312yes—
296C2×#97—32no—
297C2×C4×C8—31no—
298C2×C3×Q8—42no—
299C2×C3×Q8C22×C411yescharacteristic
300C2×C3×Q8C22×C411yescharacteristic
301C2×C3×Q8C22×C412yes—
302C22×C3×C4C22×C411yescharacteristic
303C22×C3×C4C22×C411yescharacteristic
304C22×C3×C4C22×C412yes—
305C22×C3×C4C22×C412yes—
306C22×C3×C4C2411yescharacteristic
307C2×#67C22×C412yes—
308D3×Q8—44no—
309#235—22no—
310#235—22no—
311C2×D12C22×C411yescharacteristic
312C2×C4×D3C22×C412yes—
313C2×C4×D3C22×C412yes—
314C2×C4×D3C22×C414yes—
315C2×C4×D3C22×C414yes—
316C2×C4×D3C2412yes—
317C2×Dic6C22×C411yescharacteristic
318C2×Dic6C22×C412yes—
319C2×Dic6C22×C414yes—
320C2×Dic6C22×C414yes—
321C2×Dic6C22×C412yes—
322C3×M16—22no—
323C3×M16—24no—
324C3×M16—22no—
325C2×C3×C8C2412yes—
326C2×C3×C8C2414yes—
327C2×C3×C8C2412yes—
328C3×C4⋊C4C22×C412yes—
329C3×C4⋊C4C22×C411yescharacteristic
330C3×C4⋊C4C22×C412yes—
331C3×C4⋊C4C22×C411yescharacteristic
332C3×C4⋊C4C22×C412yes—
333C3×C4⋊C4C22×C412yes—
334C3×C4⋊C4C22×C412yes—
335C3×C42C22×C412yes—
336C3×C42C22×C411yescharacteristic
337C3×C42C22×C411yescharacteristic
338C3×C42C22×C412yes—
339C3×C42C2411yescharacteristic
340C3×C42C2411yescharacteristic
341C3×C42C2412yes—
342C3×C42C2412yes—
343#217C22×C414yes—
344#217C22×C412yes—
345(C2×D3)⋊C4C22×C414yes—
346(C2×D3)⋊C4C22×C412yes—
347(C2×D3)⋊C4C22×C414yes—
348(C2×D3)⋊C4C22×C412yes—
349C4⋊Dic3C22×C411yescharacteristic
350C4⋊Dic3C22×C412yes—
351C4⋊Dic3C22×C412yes—
352C4⋊Dic3C22×C411yescharacteristic
353C4⋊Dic3C22×C414yes—
354C4⋊Dic3C22×C412yes—
355C4⋊Dic3C22×C414yes—
356C4⋊Dic3C22×C412yes—
357Dic3⋊C4C22×C414yes—
358Dic3⋊C4C22×C412yes—
359Dic3⋊C4C22×C414yes—
360Dic3⋊C4C22×C412yes—
361Dic3⋊C4C22×C414yes—
362Dic3⋊C4C22×C414yes—
363Dic3⋊C4C22×C414yes—
364Dic3⋊C4C22×C414yes—
365Dic3⋊C4C22×C414yes—
366Dic3⋊C4C22×C414yes—
367C4×Dic3C22×C412yes—
368C4×Dic3C22×C414yes—
369C4×Dic3C22×C414yes—
370C4×Dic3C22×C412yes—
371C4×Dic3C2412yes—
372C4×Dic3C2414yes—
373C2×C3⋊C8—22no—
374C2×C3⋊C8—24no—
375C2×C3⋊C8—22no—
376C2×C3⋊C8C2411yescharacteristic
377C2×C3⋊C8C2411yescharacteristic
378C2×C3⋊C8C2411yescharacteristic
379C2×C3⋊C8C2411yescharacteristic
380C2×C3⋊C8C2412yes—
381C2×C3⋊C8C2412yes—
382C2×#41—31no—
383C22×Q8—32no—
384C22×Q8C4×D311yescharacteristic
385C2×M16C22×D311yescharacteristic
386C2×M16C22×D311yescharacteristic
387C2×M16C22×D312yes—
388C22×C8—31no—
389C22×C8—31no—
390C22×C8—32no—
391C4⋊Q8—32no—
392C4⋊Q8—34no—
393C4⋊Q8—32no—
394C4⋊Q8—34no—
395C4⋊Q8—31no—
396C4⋊Q8—32no—
397C4⋊Q8—31no—
398C4⋊Q8—32no—
399#125—34no—
400#125—34no—
401#125—34no—
402#125—32no—
403#125—32no—
404#125—32no—
405C22⋊Q8—32no—
406C22⋊Q8—34no—
407C22⋊Q8—32no—
408C22⋊Q8—34no—
409C22⋊Q8—32no—
410C22⋊Q8—34no—
411C22⋊Q8—32no—
412C22⋊Q8—34no—
413C22⋊Q8—34no—
414C22⋊Q8—34no—
415C22⋊Q8—34no—
416C4×Q8—32no—
417C4×Q8—32no—
418C4×Q8—34no—
419C4×Q8—31no—
420C4×Q8—32no—
421C4×Q8—31no—
422C4×Q8—32no—
423C4×Q8—32no—
424C4×Q8—34no—
425C4×Q8—32no—
426C4×Q8—34no—
427C4×Q8C4×D311yescharacteristic
428C4×Q8C4×D311yescharacteristic
429C4×Q8C4×D312yes—
430C4×Q8C22×D311yescharacteristic
431C4×Q8C22×D311yescharacteristic
432C4×Q8C22×D312yes—
433C4×D4—32no—
434C4×D4—34no—
435C4×D4—32no—
436C4×D4—34no—
437C4×D4—31no—
438C4×D4—32no—
439C4×D4—31no—
440C4×D4—32no—
441#117—31no—
442#117—32no—
443#117—32no—
444#117—34no—
445C2×C4⋊C4—32no—
446C2×C4⋊C4—34no—
447C2×C4⋊C4C4×D311yescharacteristic
448C2×C4⋊C4C4×D312yes—
449C2×C42—32no—
450C2×C42—34no—
451C2×C42C22×D311yescharacteristic
452C2×C42C22×D312yes—
453C4⋊C8—32no—
454C4⋊C8—32no—
455C4⋊C8—32no—
456C4⋊C8—32no—
457C4⋊C8—34no—
458C4⋊C8—34no—
459C4⋊C8—34no—
460C4⋊C8—34no—
461C4⋊C8—31no—
462C4⋊C8—32no—
463C4⋊C8—31no—
464C4⋊C8—32no—
465C4⋊C8—32no—
466C4⋊C8—32no—
467C4⋊C8—32no—
468C4⋊C8C22×D312yes—
469C4⋊C8C22×D314yes—
470C4⋊C8C22×D312yes—
471C4⋊C8C22×D314yes—
472C22⋊C8—32no—
473C22⋊C8—32no—
474C22⋊C8—34no—
475C22⋊C8—34no—
476C22⋊C8—32no—
477C22⋊C8—32no—
478#97—34no—
479#97—34no—
480#97—34no—
481#97—32no—
482#97—32no—
483#97—32no—
484#97—32no—
485#97C22×D314yes—
486#97C22×D312yes—
487C4×C8—34no—
488C4×C8—34no—
489C4×C8—34no—
490C4×C8—31no—
491C4×C8—31no—
492C4×C8—31no—
493C4×C8—31no—
494C4×C8C22×D312yes—
495C4×C8C22×D314yes—
496C23×C3C23×C411yescharacteristic
497C22×D3C23×C412yes—
498C3×Q8—22no—
499C3×Q8—22no—
500C3×Q8—42no—
501C2×C3×C4—22no—
502C2×C3×C4—41no—
503C2×C3×C4—42no—
504C2×C3×C4—42no—
505C2×C3×C4C23×C411yescharacteristic
506C2×C3×C4C23×C412yes—
507C2×C3×C4C23×C412yes—
508C2×C3×C4C23×C411yescharacteristic
509C2×C3×C4C23×C412yes—
510C2×C3×C4C23×C411yescharacteristic
511C2×C3×C4C23×C412yes—
512C2×C3×C4C23×C411yescharacteristic
513C2×C3×C4C23×C411yescharacteristic
514C2×C3×C42−1+412yes—
515C2×C3×C42−1+412yes—
516C2×C3×C4C2511yescharacteristic
517#67—24no—
518C2×Dic3C23×C412yes—
519C2×Dic3C23×C414yes—
520C2×Dic3C23×C412yes—
521C2×Dic3C23×C414yes—
522C2×Dic3C23×C412yes—
523D12—22no—
524C4×D3—24no—
525C4×D3—22no—
526C4×D3—22no—
527C4×D3—42no—
528C4×D3—44no—
529C4×D3—44no—
530Dic6—22no—
531Dic6—24no—
532Dic6—44no—
533Dic6—42no—
534Dic6—44no—
535C3×C8—22no—
536C3×C8—22no—
537C3×C8—24no—
538C3⋊C8—21no—
539C3⋊C8—21no—
540C3⋊C8—22no—
541C3⋊C8—22no—
542C3⋊C8—21no—
543C3⋊C8—21no—
544#41—62no—
545#41—62no—
546C2×Q8—31no—
547C2×Q8—32no—
548C2×Q8—34no—
549C2×Q8—32no—
550C2×Q8—34no—
551C2×Q8—42no—
552C2×Q8—124no—
553C2×Q8C2×C4×D311yescharacteristic
554C2×Q8C2×C4×D311yescharacteristic
555C2×Q8C2×C4×D312yes—
556C2×D4—32no—
557C2×D4—31no—
558C22×C4—32no—
559C22×C4—32no—
560C22×C4—32no—
561C22×C4—34no—
562C22×C4—34no—
563C22×C4C2×C4×D311yescharacteristic
564C22×C4C2×C4×D311yescharacteristic
565C22×C4C2×C4×D312yes—
566C22×C4C2×C4×D312yes—
567C22×C4C23×D311yescharacteristic
568M16—22no—
569M16—22no—
570M16—24no—
571C2×C8—31no—
572C2×C8—32no—
573C2×C8—32no—
574C2×C8—31no—
575C2×C8—31no—
576C2×C8—31no—
577C2×C8—62no—
578C2×C8—64no—
579C2×C8—62no—
580C2×C8C23×D314yes—
581C2×C8C23×D312yes—
582C2×C8C23×D312yes—
583C4⋊C4—34no—
584C4⋊C4—34no—
585C4⋊C4—34no—
586C4⋊C4—34no—
587C4⋊C4—32no—
588C4⋊C4—32no—
589C4⋊C4—34no—
590C4⋊C4—32no—
591C4⋊C4—34no—
592C4⋊C4—31no—
593C4⋊C4—32no—
594C4⋊C4—31no—
595C4⋊C4—32no—
596C4⋊C4—34no—
597C4⋊C4—34no—
598C4⋊C4—34no—
599C4⋊C4—34no—
600C4⋊C4—32no—
601C4⋊C4C2×C4×D312yes—
602C4⋊C4C2×C4×D311yescharacteristic
603C4⋊C4C2×C4×D312yes—
604C4⋊C4C2×C4×D312yes—
605C4⋊C4C2×C4×D312yes—
606C4⋊C4C2×C4×D312yes—
607C4⋊C4C2×C4×D311yescharacteristic
608C22⋊C4—32no—
609C22⋊C4—34no—
610C22⋊C4—32no—
611C22⋊C4—34no—
612C22⋊C4—32no—
613C22⋊C4—34no—
614C42—32no—
615C42—34no—
616C42—34no—
617C42—32no—
618C42—34no—
619C42—32no—
620C42C2×C4×D311yescharacteristic
621C42C2×C4×D312yes—
622C42C2×C4×D312yes—
623C42C2×C4×D311yescharacteristic
624C42C23×D311yescharacteristic
625C42C23×D311yescharacteristic
626C42C23×D312yes—
627C42C23×D312yes—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3#51912yes—
631C22×C3C24×C411yescharacteristic
632C2×D3—22no—
633C2×D3—22no—
634C2×D3—22no—
635C3×C4—22no—
636C3×C4—21no—
637C3×C4—22no—
638C3×C4—21no—
639C3×C4—22no—
640C3×C4—21no—
641C3×C4—22no—
642C3×C4#51912yes—
643C3×C4#56812yes—
644C3×C4C2×2−1+411yescharacteristic
645C3×C4C2×2−1+411yescharacteristic
646Dic3—22no—
647Dic3—24no—
648Dic3—22no—
649Dic3—22no—
650Dic3—24no—
651C23—32no—
652C23C22×C4×D311yescharacteristic
653Q8—22no—
654Q8—22no—
655Q8—42no—
656Q8—64no—
657Q8—62no—
658Q8—124no—
659Q8—122no—
660Q8—124no—
661D4—64no—
662D4—62no—
663C2×C4—22no—
664C2×C4—32no—
665C2×C4—32no—
666C2×C4—34no—
667C2×C4—34no—
668C2×C4—32no—
669C2×C4—42no—
670C2×C4—41no—
671C2×C4—42no—
672C2×C4—62no—
673C2×C4—62no—
674C2×C4—64no—
675C2×C4—124no—
676C2×C4—122no—
677C2×C4—124no—
678C2×C4C22×C4×D311yescharacteristic
679C2×C4C22×C4×D312yes—
680C2×C4C22×C4×D312yes—
681C2×C4C22×C4×D311yescharacteristic
682C2×C4C22×C4×D312yes—
683C2×C4C22×C4×D311yescharacteristic
684C2×C4C22×C4×D312yes—
685C2×C4C22×C4×D311yescharacteristic
686C2×C4C22×C4×D311yescharacteristic
687C2×C4#100712yes—
688C2×C4#101012yes—
689C2×C4C24×D311yescharacteristic
690C8—22no—
691C8—24no—
692C8—22no—
693C8—61no—
694C8—62no—
695C8—62no—
696C8—61no—
697C8—61no—
698C8—61no—
699C2×C3—22no—
700C2×C3C2×#51911yescharacteristic
701C2×C3C2×#56811yescharacteristic
702C2×C3#357311yescharacteristic
703D3—42no—
704C22—21no—
705C22—21no—
706C22—62no—
707C22—62no—
708C22—62no—
709C22#557212yes—
710C22C23×C4×D311yescharacteristic
711C4—21no—
712C4—22no—
713C4—22no—
714C4—21no—
715C4—22no—
716C4—21no—
717C4—22no—
718C4—62no—
719C4—62no—
720C4—64no—
721C4—64no—
722C4—62no—
723C4#557212yes—
724C4#574512yes—
725C4C2×#100711yescharacteristic
726C4C2×#101011yescharacteristic
727C3#6025411yescharacteristic, complemented, Sylow
728C2—22no—
729C2—122no—
730C2C2×#557211yescharacteristic
731C2C2×#574511yescharacteristic
732C2#8716611yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D3
commutator, socleC22×C3C24×C4
FittingC3×Q8×M16C2
prime radicalC2×#235C23
cosocleC2×C3×C4C25
hypercenterQ8×M16D3
hypocenterC3#60254
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ Q8×M16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C3×Q8×M16C2semidirect
3. C2×#5024C2semidirect
4. #79968C2semidirect
5. #79966C2semidirect
6. #79964C2semidirect
7. #79963C2semidirect
8. #79923C2semidirect
9. #79922C2semidirect
10. #79045C2semidirect
11. #79044C2semidirect
16. #78508C2semidirect
17. #78508C2semidirect
100. Q8×M16D3semidirect
727. C3#60254semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
Q8×#2352
C3×Q8×M162
C2×#50242
#799682
#799662
#799642
#799632
#799232
#799222
#790452
#790442
#790402
#785202
#785192
#785082
#602543